具有两个和十二个基本风味的SU(3)计量系统的连续$\beta$函数

A. Hasenfratz, O. Witzel
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引用次数: 10

摘要

如果在计算期望值的过程中加入粗粒度步骤,则梯度流变换可以解释为连续的实空间重整化群变换。该方法可以预测强耦合系统的关键性质,包括重整化群$\beta$函数和非摄动不动点的异常维数。在这篇文章中,我们讨论了基于这种方法的SU(3)规范理论中$N_f=2$和$N_f=12$基本口味的连续重整化群$\beta$函数的新分析。我们遵循arXiv:1910.06408中为$N_f=2$系统开发和测试的方法。在这里,我们提供进一步的分析信息,强调连续$\beta$函数计算的鲁棒性和直观特征。我们还讨论了连续$\beta$函数计算在共形系统中的适用性,扩展了可能的相图以包括4-费米子相互作用。对$N_f=12$的数值分析使用与arXiv:1909.05842中为阶跃缩放函数生成和分析的集合相同。新的分析使用$L \ge 20$的体积,并确定$c=0$梯度流重整方案中的$\beta$函数。连续的$\beta$函数预测了保形不动点的存在,并且在不同的算子之间是一致的。虽然步进缩放和连续$\beta$函数的确定使用不同的重整化方案,但它们都预测$g^2\sim 6$周围存在保形不动点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Continuous $\beta$ function for the SU(3) gauge systems with two and twelve fundamental flavors
The gradient flow transformation can be interpreted as continuous real-space renormalization group transformation if a coarse-graining step is incorporated as part of calculating expectation values. The method allows to predict critical properties of strongly coupled systems including the renormalization group $\beta$ function and anomalous dimensions at nonperturbative fixed points. In this contribution we discuss a new analysis of the continuous renormalization group $\beta$ function for $N_f=2$ and $N_f=12$ fundamental flavors in SU(3) gauge theories based on this method. We follow the approach developed and tested for the $N_f=2$ system in arXiv:1910.06408. Here we present further information on the analysis, emphasizing the robustness and intuitive features of the continuous $\beta$ function calculation. We also discuss the applicability of the continuous $\beta$ function calculation in conformal systems, extending the possible phase diagram to include a 4-fermion interaction. The numerical analysis for $N_f=12$ uses the same set of ensembles that was generated and analyzed for the step scaling function in arXiv:1909.05842. The new analysis uses volumes with $L \ge 20$ and determines the $\beta$ function in the $c=0$ gradient flow renormalization scheme. The continuous $\beta$ function predicts the existence of a conformal fixed point and is consistent between different operators. Although determinations of the step scaling and continuous $\beta$ function use different renormalization schemes, they both predict the existence of a conformal fixed point around $g^2\sim 6$.
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